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Kinematic Concepts - Detailed Help

Sublevel 2: Distance and Displacement

Objectives:
  • The student should be able to distinguish between the quantities distance and displacement in terms of their definition and their distinction as scalars and vectors.
  • The student should be able to apply the distinction between distance and displacement to a physical scenario in order to determine the displacement and the distance of a moving object.

 

Reading:

The Physics Classroom, One-Dimensional Kinematics Unit, Lesson 1, Part c
In terms of their definitions, an essential difference between displacement and distance is that ____.
Definition of Distance:
The distance traveled by a moving object is simply the amount of ground which is covered during the motion.
Definition of Displacement:
The displacement of a moving object is the overall change in position of the object.

Suppose that a person walks 12 meters, east and then 4 meters, west. The distance traveled is 16 meters. The fact that there was a direction change is irrelevant to any measurement of the distance. The displacement of the object is 8 meters, east. The fact that there is a direction change must be considered when measuring the displacement. Displacement must account for the fact that the 4 meter segment of the motion was in the opposite direction of the 12 meter segment. For the displacement measurement, the 4 meters is considered as a negative (a directional adjective) and added onto the +12 meters.

Displacement describes how far out of place an object is when comparing its initial and final positions. Displacement is a vector quantity which is always conscious of the direction of motion and any changes in that direction. Distance is a scalar quantity which is ignorant of the<u direction of travel and any changes in direction.
For any given motion, the distance is ____.
Definition of Distance:
The distance traveled by a moving object is simply the amount of ground which is covered during the motion.
Distance is a scalar quantity which is ignorant of the direction of travel and any changes in direction. Suppose that a person walks 12 meters, east and then 4 meters, west. The distance traveled is 16 meters. The fact that there was a direction change is irrelevant to any measurement of the distance. The numerical value for the individual distances of each leg of the trip are simply added together as numbers.
For any given motion, displacement is ____.
Definition of Displacement:
The displacement of a moving object is the overall change in position of the object.
Displacement is a vector quantity which is always conscious of the direction of motion and any changes in that direction. Suppose that a person walks 12 meters, east and then 4 meters, west. The displacement of the object is 8 meters, east. The fact that there is a direction change must be considered when measuring the displacement. Displacement must account for the fact that the 4 meter segment of the motion was in the opposite direction of the 12 meters. For the displacement measurement, the 4 meters is considered as a negative (a directional adjective) and added onto the +12 meters.

A teacher does the following:

i. walks 2 m, south

ii. walks 4 m, east

iii. walks 2 m, north

iv. walks 4 m, west.

The overall displacement of the teacher is ____.
Definition of Displacement:
The displacement of a moving object is the overall change in position of the object.
Displacement is a vector quantity which is always conscious of the direction of motion and any changes in that direction. Distance is a scalar quantity which is ignorant of the direction of travel and any changes in direction. Suppose that a person walks 12 meters, east and then 4 meters, west. The distance traveled is 16 meters. The displacement of the object is 8 meters, east. The fact that there is a direction change must be considered when measuring the displacement. Displacement must account for the fact that the 4 meter segment of the motion was in the opposite direction of the 12 meters. For the displacement measurement, the 4 meters is considered as a negative (a directional adjective) and added onto the +12 meters.
In this question, the motion can be broken into four separate parts. To assist in visualizing the situation, it is always a wise idea to construct a diagram. On a piece of scrap paper, pick a starting point and label it start. Sketch out the four parts of the motion using lines with arrowheads. North would be up on the page (using the customary map convention). East would be to the right on the page; west is left and south is down. As you draw, think about the motion - the length of each part of the motion and how the overall position is changing from the labeled starting position.
Grandma Henderson challenges Michael Johnson in the 400-meter dash. Grandma H spins her wheelchair wheels five times and gives up 15 meters from the starting line. MJ makes a complete circle around the track and stops at the starting line. In this race, ____.
Definition of Displacement:
The displacement of a moving object is the overall change in position of the object.
Definition of Distance:
The distance traveled by a moving object is simply the amount of ground which is covered during the motion.

Displacement describes how far out of place an object is when comparing its initial and final positions. Displacement is a vector quantity which is always conscious of the direction of motion and any changes in that direction. Distance is a scalar quantity which is ignorant of the direction of travel and any changes in direction.

Suppose that a person walks 12 meters, east and then 4 meters, west. The distance traveled is 16 meters. The fact that there was a direction change is irrelevant to any measurement of the distance. The displacement of the object is 8 meters, east. The fact that there is a direction change must be considered when measuring the displacement. Displacement must account for the fact that the 4 meter segment of the motion was in the opposite direction as the 12 meter segment. For the displacement measurement, the 4 meters is considered as a negative (a directional adjective) and added onto the +12 meters.
If a person does a round-trip motion and finishes at the starting position, then that person does not experience any overall change in position. Overall, the person has not been displaced or moved out of place when considering the initial and the final position. While the person may have a large distance of travel - moved over a lot of ground, there is no overall displacement or change in position.
A football coach starts at the 10-yard line (A) and walks to the 40-yard line (B). He turns around and walks to the 0-yard line (C). He turns around again and walks back to the 50-yard line (D). He turns around once more and walks back to the 25-yard line (E), thus completing his 10 minutes of pacing. The coach's overall distance is ____.
Definition of Distance:
The distance traveled by a moving object is simply the amount of ground which is covered during the motion.
Distance is a scalar quantity which is ignorant of the direction of travel and any changes in direction. Suppose that a person walks 12 meters, east and then 4 meters, west. The distance traveled is 16 meters. The fact that there was a direction change is irrelevant to any measurement of the distance. The numerical value for the individual distances of each leg of the trip are simply added together as numbers.
Most physics teachers would never think of answering this question without writing something down. You will have to add four numbers together to determine the result. The numbers which are added are the individual distance values for each leg of the trip. The mathematics is simple addition; but by the time you determine the distance for the third leg of the trip, you could easily forget what the sum of the first two legs of the trip was. It would be a bright idea to write the numbers down in an organized fashion.
A football coach starts at the 10-yard line (A) and walks to the 40-yard line (B) in 3 minutes. He turns around and walks to the 0-yard line (C) in the next 2 minutes. He turns around again and walks back to the 50-yard line (D) in the next three minutes. He turns around once more and walks back to the 25-yard line (E) in the next two minutes, thus completing his 10 minutes of pacing. The coach's overall displacement is ____.
Definition of Displacement:
The displacement of a moving object is the overall change in position of the object.
Displacement is a vector quantity which is always conscious of the direction of motion and any changes in that direction. Distance is a scalar quantity which is ignorant of the direction of travel and any changes in direction. Suppose that a person walks 12 meters, east and then 4 meters, west. The distance traveled is 16 meters. The displacement of the object is 8 meters, east. The fact that there is a direction change must be considered when measuring the displacement. Displacement must account for the fact that the 4 meter segment of the motion was in the opposite direction of the 12 meters. For the displacement measurement, the 4 meters is considered as a negative (a directional adjective) and added onto the +12 meters.
Displacement is simply the overall change in position of the object. For a multi-leg trip such as this one, it can be determined by adding all the individual displacements (direction included) for each leg of the trip. But there is a far better way! Being the overall change in position, the displacement can be determined by simply determining how far out of place the final position is from the initial position. Consider only beginning and end positions and find the difference between these two positions. Include direction in your answer since displacement is a vector.